A person borrowed ₹ 9,000 at 7%, ₹ 12,000 at 8% and ₹ 15,000 at 9% simple interest per annum. He had to pay ₹ 50,700 at the end of n years. What is the value of n ?
Given: A person borrowed ₹ 9,000 at 7% simple interest borrowed ₹ 12,000 at 8% simple interest borrowed ₹ 15,000 at 9% simple interest Time =n years Amount to be paid =₹50,700 Formual Used: Simple Interst =PRT∕100 Amount = Principal + Simple Interest Calculation: Simple interest on the 9000[S1] S1=(9000×7×n)∕100=630n A1=9000+630n⋯−(i) Where A1 is the amount on 12000 Simple interest on the 12000[S2] S2=(12000×8×n)∕100=960n A2=12000+960n−⋯ (ii) Where A2 is the amount on 12000 Simple interest on the 15000[S3] S3=(15000×9×n)∕100=1350n A3=15000+1350n⋯ (iii) Where A3 is the amount on 15000 Now from (i), (ii) and (iii), we get 9000+630n+12000+960n+15000+1350n=50,700 ⇒2940n+36000=50700 ⇒2940n=14700 ⇒n=5 ∴ The required time is 5 years.